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- La ecuación:
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Ecuación y^2-5*y=0
-
Ecuación 49x^3+14x^2+x=0
-
Ecuación x-12=0
-
Ecuación (x-3)/(x+1)=0
- Expresar {x} en función de y en la ecuación:
- -16*x+3*y=17
- 18*x-14*y=-2
- 18*x+19*y=10
- 11*x-6*y=5
- Derivada de:
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1/4
- Suma de la serie:
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1/4
- Integral de d{x}:
- 1/4
-
Expresiones idénticas
- (log[sinx*cosx,sinx])*(log[sinx*cosx,sinx*cosx])= uno / cuatro
- ( logaritmo de [ seno de x multiplicar por coseno de x, seno de x]) multiplicar por ( logaritmo de [ seno de x multiplicar por coseno de x, seno de x multiplicar por coseno de x]) es igual a 1 dividir por 4
- ( logaritmo de [ seno de x multiplicar por coseno de x, seno de x]) multiplicar por ( logaritmo de [ seno de x multiplicar por coseno de x, seno de x multiplicar por coseno de x]) es igual a uno dividir por cuatro
- (log[sinxcosx,sinx])(log[sinxcosx,sinxcosx])=1/4
- log[sinxcosx,sinx]log[sinxcosx,sinxcosx]=1/4
- (log[sinx*cosx,sinx])*(log[sinx*cosx,sinx*cosx])=1 dividir por 4
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Expresiones semejantes
- 1/(4*sh(z-1))=1/(z^2-6*z+5)
- (x-3)/(x+2)+(x+2)/(x-3)=-4(1)/(4)
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Expresiones con funciones
- Logaritmo log
- log(y)=x^5/5
- log(x,10)=-2,3
- log_6(6x+3)=1-log_6(x+2)
- log2(27)*x=1/3
- log(x,5)^2+log(5\x,5x)=1
- Logaritmo log
- log(y)=x^5/5
- log(x,10)=-2,3
- log_6(6x+3)=1-log_6(x+2)
- log2(27)*x=1/3
- log(x,5)^2+log(5\x,5x)=1
(log[sinx*cosx,sinx])*(log[sinx*cosx,sinx*cosx])=1/4 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
log(sin(x)*cos(x), sin(x))*log(sin(x)*cos(x), sin(x)*cos(x)) = 1/4
$$\log{\left(\sin{\left(x \right)} \cos{\left(x \right)} \right)} \log{\left(\sin{\left(x \right)} \cos{\left(x \right)} \right)} = \frac{1}{4}$$
Solución detallada
Tenemos la ecuación
$$\log{\left(\sin{\left(x \right)} \cos{\left(x \right)} \right)} \log{\left(\sin{\left(x \right)} \cos{\left(x \right)} \right)} = \frac{1}{4}$$
cambiamos
$$- \frac{1}{4} + \frac{\log{\left(\frac{\sin{\left(2 x \right)}}{2} \right)}}{\log{\left(\sin{\left(x \right)} \right)}} = 0$$
$$\log{\left(\sin{\left(x \right)} \cos{\left(x \right)} \right)} \log{\left(\sin{\left(x \right)} \cos{\left(x \right)} \right)} - \frac{1}{4} = 0$$
Sustituimos
$$w = \cos{\left(x \right)}$$
Tenemos la ecuación
$$\frac{\log{\left(w \sin{\left(x \right)} \right)}}{\log{\left(\sin{\left(x \right)} \right)}} - \frac{1}{4} = 0$$
$$\frac{\log{\left(w \sin{\left(x \right)} \right)}}{\log{\left(\sin{\left(x \right)} \right)}} = \frac{1}{4}$$
Devidimos ambás partes de la ecuación por el multiplicador de log =1/log(sin(x))
$$\log{\left(w \sin{\left(x \right)} \right)} = \frac{\log{\left(\sin{\left(x \right)} \right)}}{4}$$
Es la ecuación de la forma:
Por definición log
entonces
$$w \sin{\left(x \right)} = e^{\frac{1}{4 \frac{1}{\log{\left(\sin{\left(x \right)} \right)}}}}$$
simplificamos
$$w \sin{\left(x \right)} = \sqrt[4]{\sin{\left(x \right)}}$$
$$w = \frac{1}{\sin^{\frac{3}{4}}{\left(x \right)}}$$
hacemos cambio inverso
$$\cos{\left(x \right)} = w$$
Tenemos la ecuación
$$\cos{\left(x \right)} = w$$
es la ecuación trigonométrica más simple
Esta ecuación se reorganiza en
$$x = \pi n + \operatorname{acos}{\left(w \right)}$$
$$x = \pi n + \operatorname{acos}{\left(w \right)} - \pi$$
O
$$x = \pi n + \operatorname{acos}{\left(w \right)}$$
$$x = \pi n + \operatorname{acos}{\left(w \right)} - \pi$$
, donde n es cualquier número entero
sustituimos w:
$$\log{\left(\sin{\left(x \right)} \cos{\left(x \right)} \right)} \log{\left(\sin{\left(x \right)} \cos{\left(x \right)} \right)} = \frac{1}{4}$$
cambiamos
$$- \frac{1}{4} + \frac{\log{\left(\frac{\sin{\left(2 x \right)}}{2} \right)}}{\log{\left(\sin{\left(x \right)} \right)}} = 0$$
$$\log{\left(\sin{\left(x \right)} \cos{\left(x \right)} \right)} \log{\left(\sin{\left(x \right)} \cos{\left(x \right)} \right)} - \frac{1}{4} = 0$$
Sustituimos
$$w = \cos{\left(x \right)}$$
Tenemos la ecuación
$$\frac{\log{\left(w \sin{\left(x \right)} \right)}}{\log{\left(\sin{\left(x \right)} \right)}} - \frac{1}{4} = 0$$
$$\frac{\log{\left(w \sin{\left(x \right)} \right)}}{\log{\left(\sin{\left(x \right)} \right)}} = \frac{1}{4}$$
Devidimos ambás partes de la ecuación por el multiplicador de log =1/log(sin(x))
$$\log{\left(w \sin{\left(x \right)} \right)} = \frac{\log{\left(\sin{\left(x \right)} \right)}}{4}$$
Es la ecuación de la forma:
log(v)=p
Por definición log
v=e^p
entonces
$$w \sin{\left(x \right)} = e^{\frac{1}{4 \frac{1}{\log{\left(\sin{\left(x \right)} \right)}}}}$$
simplificamos
$$w \sin{\left(x \right)} = \sqrt[4]{\sin{\left(x \right)}}$$
$$w = \frac{1}{\sin^{\frac{3}{4}}{\left(x \right)}}$$
hacemos cambio inverso
$$\cos{\left(x \right)} = w$$
Tenemos la ecuación
$$\cos{\left(x \right)} = w$$
es la ecuación trigonométrica más simple
Esta ecuación se reorganiza en
$$x = \pi n + \operatorname{acos}{\left(w \right)}$$
$$x = \pi n + \operatorname{acos}{\left(w \right)} - \pi$$
O
$$x = \pi n + \operatorname{acos}{\left(w \right)}$$
$$x = \pi n + \operatorname{acos}{\left(w \right)} - \pi$$
, donde n es cualquier número entero
sustituimos w:
Respuesta numérica
[src]
x1 = 4.31683269777069 - 0.715534032132015*i
x2 = 42.0159445408482 - 0.715534032132015*i
x3 = 29.449573926489 - 0.715534032132015*i
x4 = -14.5327232237681 + 0.715534032132015*i
x5 = 10.6000180049503 - 0.715534032132015*i
x6 = -71.0813909883843 + 0.715534032132015*i
x7 = -58.5150203740252 + 0.715534032132015*i
x8 = 92.2814269982849 + 0.715534032132015*i
x9 = 73.4318710767461 - 0.715534032132015*i
x10 = 60.865500462387 + 0.715534032132015*i
x11 = -33.3822791453068 + 0.715534032132015*i
x12 = -30.7170572685777 - 0.653476165722081*i
x13 = 67.1486857695666 + 0.715534032132015*i
x14 = 13.2652398816794 - 0.653476165722081*i
x15 = 54.5823151552074 + 0.715534032132015*i
x16 = -64.7982056812048 + 0.715534032132015*i
x17 = -39.6654644524864 - 0.715534032132015*i
x18 = -64.7982056812048 - 0.715534032132015*i
x19 = 98.5646123054645 + 0.715534032132015*i
x20 = 35.7327592336686 - 0.715534032132015*i
x21 = -20.8159085309477 + 0.715534032132015*i
x22 = -45.948649759666 + 0.715534032132015*i
x23 = 23.1663886193095 + 0.715534032132015*i
x24 = 48.2991298480278 + 0.715534032132015*i
x25 = 16.8832033121299 + 0.715534032132015*i
x26 = -83.6477616027435 - 0.715534032132015*i
x27 = -1.96635260940889 - 0.715534032132015*i
x28 = 57.2475370319365 - 0.653476165722081*i
x29 = 48.2991298480278 - 0.715534032132015*i
x30 = 98.5646123054645 - 0.715534032132015*i
x31 = -8.24953791658848 - 0.715534032132015*i
x32 = -27.0990938381272 + 0.715534032132015*i
x33 = 85.9982416911053 + 0.715534032132015*i
x34 = -89.9309469099231 - 0.715534032132015*i
x35 = -77.3645762955639 - 0.715534032132015*i
x36 = -45.948649759666 - 0.715534032132015*i
x37 = 85.9982416911053 - 0.715534032132015*i
x38 = -14.5327232237681 - 0.715534032132015*i
x39 = 73.4318710767461 + 0.715534032132015*i
x40 = 54.5823151552074 - 0.715534032132015*i
x41 = -77.3645762955639 + 0.715534032132015*i
x42 = 79.7150563839257 - 0.715534032132015*i
x43 = -52.2318350668456 - 0.715534032132015*i
x44 = -39.6654644524864 + 0.715534032132015*i
x45 = -20.8159085309477 - 0.715534032132015*i
x46 = 23.1663886193095 - 0.715534032132015*i
x47 = -96.2141322171027 - 0.715534032132015*i
x48 = 79.7150563839257 + 0.715534032132015*i
x48 = 79.7150563839257 + 0.715534032132015*i